David et. al:

I take issue with this. It is the lack of independence that is the major
issue. In particular, clustering, split-plotting, and so forth due to
"convenience order" experimentation, lack of randomization, exogenous
effects like the systematic effects due to measurement method/location have
the major effect on inducing bias and distorting inference. Normality and
unequal variances typically pale to insignificance compared to this.

Obviously, IMHO.

Note 1: George Box noted this at least 50 years ago in the early '60's when
he and Jenkins developed arima modeling.

Note 2: If you can, have a look at Jack Youden's classic paper "Enduring
Values", which comments to some extent on these issues, here:
http://www.jstor.org/pss/1266913

Cheers,
Bert


Bert Gunter
Genentech Nonclinical Biostatistics



On Mon, Aug 2, 2010 at 10:32 AM, David Winsemius <dwinsemius@comcast.net>wrote:

>
> On Aug 2, 2010, at 9:33 AM, wwreith wrote:
>
>
>> I am conducting an experiment with four independent variables each of
>> which
>> has three or more factor levels. The sample size is quite large i.e.
>> several
>> thousand. The dependent variable data does not pass a normality test but
>> "visually" looks close to normal so is there a way to compute the affect
>> this would have on the p-value for ANOVA or is there a way to perform an
>> nonparametric test in R that will handle this many independent variables.
>> Simply saying ANOVA is robust to small departures from normality is not
>> going to be good enough for my client.
>>
>
> The statistical assumption of normality for linear models do not apply to
> the distribution of the dependent variable, but rather to the residuals
> after a model is estimated. Furthermore, it is the homoskedasticity
> assumption that is more commonly violated and also greater threat to
> validity. (And if you don't already know both of these points, then you
> desperately need to review your basic modeling practices.)
>
>
>  I need to compute an error amount for
>> ANOVA or find a nonparametric equivalent.
>>
>
> You might get a better answer if you expressed the first part of that
> question in unambiguous terminology.  What is "error amount"?
>
> For the second part, there is an entire Task View on Robust Statistical
> Methods.
>
> --
>
> David Winsemius, MD
> West Hartford, CT
>
>
> ______________________________________________
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> PLEASE do read the posting guide
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> and provide commented, minimal, self-contained, reproducible code.
>

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